A variable plane forms a tetrahedron of constant volume with the coordinate planes…

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

A variable plane forms a tetrahedron of constant volume

64K^3

with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is (1)

x^3 + y^3 + z^3 = 6k^3

(2)

xyz = 6k^3

(3)

x^2 + y^2 + z^2 = 4k^2

(4)

x^{-2} + y^{-2} + z^{-2} = 4k^{-2}